Aircraft: CITATION V/ULTRA/ENCORE (C560)
Phase of flight: Initial Approach
Anomaly: Aircraft Equipment Problem Less Severe; Conflict NMAC

[We] had a MELed TCAS. We were in approach phase at UNV. We were being vectored by NY Center and setup on a high right downwind for runway 24. We had the airport insight and were cleared for a visual approach to 24 and Center mentioned that there was traffic below us and that he was not talking to him. On base leg we were still talking to NY Center and I asked how that traffic looked for us. He pointed out aircraft at our 10 O'clock low and traffic to our right on final. As I looked left for the first traffic at 10 o'clock I saw we just passed over Aircraft Y as we turned final. The other traffic on final was harder to see but he was a smaller aircraft and we had to slow way down. I asked to switch to Tower and we were handed off. Once I checked in with Tower he was asking Aircraft Y if he had us in sight to which he replied 'yes; he flew just over top of me.' We landed without further event and while taxiing back we asked Aircraft Y's pilot how close we were and he replied 300 feet. The KUNV Tower Controller called NY Center to complain about dropping us in like they did. We called ACP after shutdown to discuss our concerns of operating with an INOP TCAS. The best he could offer was to try to push for a sooner maintenance fix.The TCAS MEL is currently a 10 day MEL. It needs to be a Cat B 3 day. For the type of operational tempo we do and especially a smaller fleet like the Encore + that goes into small uncontrolled strips the situation awareness gained from a TCAS is vital. There is no doubt that if we had an operational TCAS; we would've caught on to what was happening in KUNV. This safety concern should be at the top of the list. After being cleared for the visual approach to runway 24; [we] flew over Aircraft Y aircraft by 300 feet on the same approach. We became aware something was wrong once we were established on final and contacted University Park Tower. As we switched frequency; we heard Aircraft Y checking in on the visual approach in the proximity of where we were. This raised immediate flags. With a go around imminent; the Aircraft Y pilot advised that he had us in sight ahead of him and that we had flown over him. After both aircraft were on the ground I asked the Aircraft Y pilots how close we had flown over them. That is when we realized the vertical separation had only been all but 300 feet. University Park Tower apologized to all involved and said that it was a New York Center goof-up. After shut-down; we contacted the ACP on duty; and he advise the Captain to do an OIR; and for both of us to complete an ASAP. This event happened on our second leg of a 5 leg day; and THE TCAS WAS MELed. We asked the ACP if this airplane could be pulled off of the line to have the TCAS serviced. He advised us that there were 470+ revenue flights and probably would not happen due to demand.The day prior to this event we were briefed to fly this aircraft to an uncontrolled field with a history of heavy flight training and banner towing operations. The captain had either never been there or had not been there in a very long time. I expressed my concerns to him after he briefed me that the TCAS was inoperative. This was Saturday morning with VFR weather and calm winds throughout the northeast. He asked me if I would contact the ACP since I was more familiar with the airport. I contacted the ACP on duty and I was told that it was early and that there would not be much traffic. I was also told that the airplane was legal to fly. I expressed my safety concerns; especially flying around an uncontrolled airport on a nice weather weekend. I asked if we could look at maybe sending an airplane that has TCAS into that airport but that was not an option. We pressed on and used extreme caution and landed safely. The event that happened the day after was at a tower controlled airport; which is more disturbing. My recommendation to the panel is to please push to make this a 3 day item MEL. Operating in this degraded state for 10 days is a definite safety issue; especially in the environment we fly in. If the TCAS was operational; this event would not have happened. We do not operate without weather radar in known or forecasted weather; why are we operating aircraft without TCAS where unlike weather; the threat is always there. In the mean time; if I ever take an airplane in this degraded state; I will tell ATC that my TCAS is inoperative so they are aware we can't see or have an idea where our traffic is. Citation flight crew reported NMAC at UNV due at least in part to an inoperative TCAS.